New York temperature. For any date, the average temperature in New York can be approximated by T ( x ) = 43.5 − 18.4 x + 8.57 x 2 − 0.996 x 3 + 0.0338 x 4 , where T represents the temperature in degrees Fahrenheit, x = 1 represents the middle of January, x = 2 represents the middle of February, and so on. (Source: Based on data from www.worldclimate.com. ) Compute the average temperature in New York over the whole year to the nearest degree.
New York temperature. For any date, the average temperature in New York can be approximated by T ( x ) = 43.5 − 18.4 x + 8.57 x 2 − 0.996 x 3 + 0.0338 x 4 , where T represents the temperature in degrees Fahrenheit, x = 1 represents the middle of January, x = 2 represents the middle of February, and so on. (Source: Based on data from www.worldclimate.com. ) Compute the average temperature in New York over the whole year to the nearest degree.
Solution Summary: The author calculates the average temperature in New York over the year rounded up to the nearest degree if the function T(x) = 43.5-18.4x+8.57
New York temperature. For any date, the average temperature in New York can be approximated by
T
(
x
)
=
43.5
−
18.4
x
+
8.57
x
2
−
0.996
x
3
+
0.0338
x
4
,
where T represents the temperature in degrees Fahrenheit,
x
=
1
represents the middle of January,
x
=
2
represents the middle of February, and so on. (Source: Based on data from www.worldclimate.com.) Compute the average temperature in New York over the whole year to the nearest degree.
Consider the following system of equations, Ax=b :
x+2y+3z - w = 2
2x4z2w = 3
-x+6y+17z7w = 0
-9x-2y+13z7w = -14
a. Find the solution to the system. Write it as a parametric equation. You can use a
computer to do the row reduction.
b. What is a geometric description of the solution? Explain how you know.
c. Write the solution in vector form?
d. What is the solution to the homogeneous system, Ax=0?
2. Find a matrix A with the following qualities
a. A is 3 x 3.
b. The matrix A is not lower triangular and is not upper triangular.
c. At least one value in each row is not a 1, 2,-1, -2, or 0
d. A is invertible.
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